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anonymous

6 years ago

it has a lot of formulas depending on the shape isnt it?

anonymous

6 years ago

itis the rotational analogue of mass.yeah there are.u can find out by using parallel axis theorems and perpendicular axis theorem!!

anonymous

6 years ago

i dont understand this question. Four particles A, B, C and D of mass 2 kg, 5 kg, 6 kg and 3 kg respectively are rigidly joined together by light rods to form a rectangle ABCD where AB=2a and BC=4a. Find the moment of inertia of this system of particles about an axis along AB..

More answers

anonymous

6 years ago

do i have to use I=Md\[^{2}\]

Mani_Jha

6 years ago

I had the exact same question in my mind when I started rotation. Unfortunately, none of my teachers could explain it that thouroughly. I had to do some self-research. :)
You know what is inertia, right? A more massive mass requires more force to be moved. Mass is a measure of inertia. Now, when something rotates about its axis, the amount of force required to stop it does not depend only on the mass, but also a new thing - The distance from the axis.
Try it. Try to move a stationary fan by giving it a strike it at its edge. It easily rotates. Then try to strike it somewhere near the center. It moves less. You have to apply more force to move something closer to the axis of rotation. So, now, the inertia of a rotating object is not only a function of mass, but also of the distance from the axis of rotation.
You can try to find the kinetic energy of a rotating particle. Considering angular velocity for v, you will find the kinetic energy to be:
\[mr ^{2} w ^{2}/2\].
The linear kinetic energy is
\[mv ^{2}/2\]
Compare these, and you will find that during rotation, the mass of a body is equivalent to mr^2. This new quantity is known as moment of inertia(you can clearly see moment of inertia increases with increasing distance from the axis)
Did u get this?

anonymous

6 years ago

Yeah! Great explanation.. I can finally picture it in my head.. :D bout my question i have to make the line of axis parallel to AB.. rite??

Mani_Jha

6 years ago

Yes, right. First find the moment of inertia about the centre of the system. Then use the parallel axis theorem(do u know it?)

anonymous

6 years ago

about the centre??

anonymous

6 years ago

so d=2a rite?? if from centre..

anonymous

6 years ago

sorry.. im a bit slow..

Mani_Jha

6 years ago

Wait, you can do without the parallel axis theorem. The axis is AB. Take the coordinate axis along AB(x or y). Then find the distance of the four masses from the origin. Find the moment of inertia of each, and add them up.
|dw:1331285211599:dw|
I have considered A as the origin. Use the distance formula to calculate the distance of each mass from origin, and then use I=mr^2.

Mani_Jha

6 years ago

I would like to add something to the explanation. It is more difficult to stop the edges of a rotating fan, than the points closer to the center(because they have higher moment of inertia). The edges rotate at a higher speed than the others. You can observe that. The edges will appear completely blurred in a photograph, while the points close to the centre will be more visible

anonymous

6 years ago

i have to find the inertia for A too?? even if it is the origin??

Mani_Jha

6 years ago

it will be zero

anonymous

6 years ago

|dw:1331285964516:dw|
this is from my lecturer's note.. what is with the delta x for?? and why is d the distance from the axis that we draw to the rod?? how should we know tat??
it explains that moment of inertia of typical element about XY = md2 (which i dont understand) n concluded Ixy=Md^2..

anonymous

6 years ago

bout the delta x she wrote "Divide rod into elements each of length δx.
"

Mani_Jha

6 years ago

A large part of classical mechanics(including newton's laws) deals with only particles. For a particle, we can easily say that its moment of inertia is mr^2. But not so, for large bodies.
But the best we can do is divide(i.e. differentiate) large bodies into its constituent particles. We shall find the moment of inertia for a single particle, and add up for all of them(i.e. integrate) to find the net moment of inertia for the body.
So, in the case of the rod, we have divided it into small elements of an extremely small length(we choose an extremely small length to make it equivalent to a particle) dx. The axis of rotation in a problem will always be given. You just have to find the distance of a particle from the axis.
Since the element of length dx is a particle, we can say that it's moment of inertia is mr^2.
Did u get it?

anonymous

6 years ago

from the question tat i posted, the axis is the AB.. the particle is what? Is it the origin? Can i take B as the origin?

Mani_Jha

6 years ago

A, B, C and D are all particle masses. Yes, u cant take any point as the origin. But make sure you calculate the distances correctly

anonymous

6 years ago

i cant?? But how do i noe which one to take as the origin?? the axis is AB so i shud take whether A or B as the origin.. am i rite??

Mani_Jha

6 years ago

sorry, typing mistake. You CAN take any point as the origin, but it would be more preferable to take A or B as origin because they lie on the axis

anonymous

6 years ago

What if i take C and D?? What will happen??

Mani_Jha

6 years ago

Oh wait, I was correct when I had mistyped! See AB is the axis, which means A and B are gonna remain stationary. But C and D are going to move, continously changing their positions. So, it does not make sense to take either of them as origin. So take either A or B only as origin.
This happens only in rotation. Otherwise, you CAN take any point as origin

Mandy_Nakamoto:
In simple manner moment of inertia is the mass which appose the rotational motion of any body. in the linear motion it is mass and in rotational motion it just named as moment of inertia.....the moment of inertia depends on the shape of the body.and we calculate the moment of inertia of any regular shape body by integratio method..such as moment of inertia circle is mr^2.where m is mass and r is the radius of that circle..we apply following integeration formula:
dI=dmr^2... when mass is variable and dI is the moment of inertia of small part which has mass dm.... i hope that you will get your answer....